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BartSMP [9]
3 years ago
11

In a carton of 10 eggs three were broken. Steven took 2 unbroken eggs and baked omelettes. A little later he took another egg ou

t of the carton. What is the probability that this egg was not broken?
Mathematics
1 answer:
Natali [406]3 years ago
4 0

After he got 2 unbroken eggs there were 5 unbroken ones and 3 broken. In total 8 eggs.

The probability that the egg was not broken is <u>5/8</u> or <u>62,5%</u>.

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<h2>Answer with explanation:</h2>

According to the Binomial probability distribution ,

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The probability that the whole lot is accepted :

P(X\leq 2)=P(x=0)+P(x=1)+P(x=2)\\\\=^{15}C_0(0.03)^0(0.97)^{15}+^{15}C_1(0.03)^1(0.97)^{14}+^{15}C_2(0.03)^2(0.97)^{13}\\\\=(0.97)^{15}+(15)(0.03)^1(0.97)^{14}+\dfrac{15!}{2!13!}(0.03)^2(0.97)^{13}\\\\\approx0.63325+0.29378+0.06360=0.99063

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For sample size n= 2500

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The expected value = 75

Standard deviation :  \sigma=\sqrt{np(1-p)}=\sqrt{2500(0.03)(0.97)}\approx8.53

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